# -*- coding: utf-8 -*-
"""
    Time    : 2021/1/9 下午1:45
    Author  : Thinkgamer
    File    : 123-买卖股票的最佳时机3.py
    Desc    : https://leetcode-cn.com/problems/best-time-to-buy-and-sell-stock-iii/
"""
"""
给定一个数组，它的第 i 个元素是一支给定的股票在第 i 天的价格。
设计一个算法来计算你所能获取的最大利润。你最多可以完成 两笔 交易。
注意：你不能同时参与多笔交易（你必须在再次购买前出售掉之前的股票）。

示例 1:
输入：prices = [3,3,5,0,0,3,1,4]
输出：6
解释：在第 4 天（股票价格 = 0）的时候买入，在第 6 天（股票价格 = 3）的时候卖出，这笔交易所能获得利润 = 3-0 = 3 。
     随后，在第 7 天（股票价格 = 1）的时候买入，在第 8 天 （股票价格 = 4）的时候卖出，这笔交易所能获得利润 = 4-1 = 3 。

示例 2：
输入：prices = [1,2,3,4,5]
输出：4
解释：在第 1 天（股票价格 = 1）的时候买入，在第 5 天 （股票价格 = 5）的时候卖出, 这笔交易所能获得利润 = 5-1 = 4 。  
     注意你不能在第 1 天和第 2 天接连购买股票，之后再将它们卖出。  
     因为这样属于同时参与了多笔交易，你必须在再次购买前出售掉之前的股票。

示例 3：
输入：prices = [7,6,4,3,1]
输出：0
解释：在这个情况下, 没有交易完成, 所以最大利润为 0。

示例 4：
输入：prices = [1]
输出：0
 
提示：
1 <= prices.length <= 105
0 <= prices[i] <= 105
"""


# 思路：获取在整个序列上只进行一次买卖的收益，再获取将序列分为两端的最大收益，如果大于一次的则进行替换
# 超时
def max_profit(prices):
	# 获取一段中一次买卖的最大收益
	def get_one_max_profit_v1(nums):
		_len = len(nums)
		if _len <= 1:
			return 0
		elif n == 2:
			return prices[1] - prices[0] if prices[1] - prices[0] > 0 else 0
		else:
			min_v = nums[0]
			max_v = nums[0]
			max_p = 0
			for i in range(1, _len):
				if nums[i] < min_v:
					min_v = nums[i]
					max_v = nums[i]
				elif nums[i] > max_v:
					if nums[i] - min_v > max_p:
						max_p = nums[i] - min_v
				else:
					continue
		return max_p
		
	# 获取一段中一次买卖的最大收益
	def get_one_max_profit_v2(nums):
		base = nums[0]
		result = 0
		for i in range(1, len(nums)):
			if nums[i] >= base:
				if nums[i] - base > result:
					result = nums[i] - base
			else:
				base = nums[i]
		return result
	
	n = len(prices)
	if n <= 1:
		return 0
	elif n == 2:
		return prices[1] - prices[0] if prices[1] - prices[0] > 0 else 0
	else:
		# 获取在prices中只进行一次买卖能够获取的最大收益
		max_p = get_one_max_profit_v2(prices)
		print(max_p)
		# 从第一位开始遍历，到第 n-2 位结束，以当前点作为两次买卖的分裂点，分别获取两端的最大利益，进行累加
		for i in range(1, n-2):
			# 如果 price里的是递减的或者 当前数字是连续重复的，则跳过
			if prices[i] < prices[i-1] or prices[i] == prices[i-1]:
				continue
			print(i)
			left = get_one_max_profit_v2(prices[:i+1]) if len(prices[:i+1]) > 0 else 0
			right = get_one_max_profit_v2(prices[i + 1:]) if len(prices[i+1:]) > 0 else 0
			if left + right > max_p:
				max_p = left + right
	return max_p


# 参考：https://leetcode-cn.com/problems/best-time-to-buy-and-sell-stock-iii/solution/on4you-hua-dao-on2zai-you-hua-dao-on-by-3912l/
# 使用left[i] 表示 0,..., i的最大收益， right[i] 表示 i,...,n-1的最大收益
# 648ms 60.81% | 26.4mb 54.10%
def max_profit_v2(prices):
	import sys
	n = len(prices)
	
	# 获取 left[i]
	left_min_v = sys.maxsize
	left_max_p = 0
	left = [0] * n
	for i in range(0, n):
		left_min_v = min(left_min_v, prices[i])
		left_max_p = max(left_max_p, prices[i] - left_min_v)
		left[i] = left_max_p
	
	# 获取 right[i]
	right_max_v = 0
	right_max_p = 0
	right = [0] * n
	while n > 0:
		n -= 1
		right_max_v = max(right_max_v, prices[n])
		right_max_p = max(right_max_p, right_max_v - prices[n])
		right[n] = right_max_p
	
	res = 0
	for i in range(len(left)):
		res = max(res, left[i] + right[i])
	return res


# 参考：https://leetcode-cn.com/problems/best-time-to-buy-and-sell-stock-iii/solution/mai-mai-gu-piao-de-zui-jia-shi-ji-iii-by-wrnt/
# 动态规划，定义五种状态：当天无操作（无收益），当天买入(buy1)，当天第一次买入之后的卖出(sell1)，当天完成一次买卖之后的买入(buy2)，当天完成一次买卖之后的卖出(sell2)
# 556ms 68.26% | 25mb 60.56%
def max_profit_v3(prices):
	n = len(prices)
	buy1 = buy2 = -prices[0]
	sell1 = sell2 = 0
	for i in range(1, n):
		buy1 = max(buy1, -prices[i])
		sell1 = max(sell1, buy1 + prices[i])
		buy2 = max(buy2, sell1-prices[i])
		sell2 = max(sell2, buy2 + prices[i])
	return sell2


for prices in [
	[3, 3, 5, 0, 0, 3, 1, 4],
	[1, 2, 3, 4, 5],
	[7, 6, 4, 3, 1],
	[1],
	[1, 2],
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6852,10169,18870,19870,19249,16456,14044,2113,6790,501,2058,12564,8044,5921,14762,10443,11572,7998,9315,6386,11458,15250,6144,974,10167,14066,13725,19400,849,1593,9152,11790,11291,18850,961,12550,4940,3344,17211,12115,1646,7327,18906,4025,10512,12830,1309,4712,4455,1838,4765,17952,3136,10144,9944,14899,18959,223,11371,19772,11927,16421,4986,4812,17311,19991,10730,1775,10018,11330,11294,14156,15848,9871,8743,12637,16521,17447,13757,9982,4198,4806,3374,1153,3502,9468,4160,16837,10070,9213,9849,7039,9848,208,177,15057,18068,7674,1189],
]:
	result = max_profit_v3(prices)
	print(result)
